moment reaction at A in the plane frame below is approximately:

A) $+ 1400 \mathrm {~N} \cdot \mathrm { m }$
B) $- 2280 \mathrm {~N} \cdot \mathrm { m }$
C) $- 3600 \mathrm {~N} \cdot \mathrm { m }$
D) $+ 6400 \mathrm {~N} \cdot \mathrm { m }$

Question

moment reaction at A in the plane frame below is approximately:

A) $+ 1400 \mathrm {~N} \cdot \mathrm { m }$ 
B) $- 2280 \mathrm {~N} \cdot \mathrm { m }$ 
C) $- 3600 \mathrm {~N} \cdot \mathrm { m }$ 
D) $+ 6400 \mathrm {~N} \cdot \mathrm { m }$

Quizplus · Accepted Answer

To find the moment reaction at A, we need to take moments about point A. Let's consider the clockwise moments to be positive.

$$\sum M_A = (-500\mathrm{N}\cdot2\mathrm{m}) + (-400\mathrm{N}\cdot3\mathrm{m}) + (-600\mathrm{N}\cdot5\mathrm{m}) + R_A \cdot 4\mathrm{m} = 0$$

Solving for $R_A$, we get:

$$R_A = \frac{(500\mathrm{N}\cdot2\mathrm{m}) + (400\mathrm{N}\cdot3\mathrm{m}) + (600\mathrm{N}\cdot5\mathrm{m})}{4\mathrm{m}} = +6400\mathrm{N}\cdot\mathrm{m}$$

Therefore, the moment reaction at A is +6400 N·m, which is the same as choice D.

Moment Reaction at a in the Plane Frame Below Is +1400 N⋅m+ 1400 \mathrm {~N} \cdot \mathrm { m }+1400 N⋅m

Moment Reaction at a in the Plane Frame Below Is $+ 1400 \mathrm {~N} \cdot \mathrm { m }$